YES

TRS:

  le(0(),y) -> true()
  le(s(x),0()) -> false()
  le(s(x),s(y)) -> le(x,y)
  minus(x,0()) -> x
  minus(s(x),s(y)) -> minus(x,y)
  gcd(0(),y) -> y
  gcd(s(x),0()) -> s(x)
  gcd(s(x),s(y)) -> if_gcd(le(y,x),s(x),s(y))
  if_gcd(true(),s(x),s(y)) -> gcd(minus(x,y),s(y))
  if_gcd(false(),s(x),s(y)) -> gcd(minus(y,x),s(x))

linear polynomial interpretations on N:

  le_A(x1,x2) = x1 + x2 + 1
  le#_A(x1,x2) = 1
  0_A = 1
  0#_A = 1
  true_A = 1
  true#_A = 0
  s_A(x1) = x1 + 4
  s#_A(x1) = 9
  false_A = 1
  false#_A = 0
  minus_A(x1,x2) = x1 + 1
  minus#_A(x1,x2) = 0
  gcd_A(x1,x2) = x1 + x2
  gcd#_A(x1,x2) = x1 + x2 + 2
  if_gcd_A(x1,x2,x3) = x2 + x3
  if_gcd#_A(x1,x2,x3) = x2 + x3

precedence:

  minus = if_gcd > gcd > le = 0 = s > true = false